1) Experimental studies
Experimental determination of the relative permeabilities of a porous medium wherein a multiphase fluid flows is not easy. Measuring operations are usually simplified by considering that one of the phases is immobile in a state of irreducible saturation.
The values are for example acquired by means of a well-known experimental method referred to as "steady state" for determining relative permeabilities, which consists in allowing a three-phase fluid to flow with imposed flow rates between the phases. The relative permeabilities expressed as a function of the two saturations are calculated by applying Darcy's law to each phase. It is not an established fact that the relative permeability measurements obtained by means of this method are really representative of the fluid displacements and in any case they take a long time because, at each regime change, one has to wait for a state of equilibrium.
Another known method consists in carrying out laboratory tests in order to determine measurement tables (as shown in FIG. 1) relating the relative permeabilities and the saturations for each pair of fluids of the three-phase mixture. By adjusting experimental production curves, one tries to progressively adjust the three-phase relative permeabilities. These data tables are then fed into a Score.RTM. or Athos.RTM. type numerical simulator which computes the fluid productions. This method being based on the prior acquisition of many experimental measurements progressively adjusted by calibration, it takes a long time.
Another known experimental measuring method is described for example in patents FR-A-2,708,742 or 2,724,460 filed by the applicant. It is implemented by placing in a measuring cell a bar cut in the porous medium to be studied and containing, at variable saturations for each experiment, two phases of a three-phase fluid. A third phase of this fluid is injected at one end of the bar and the production of the three phases as a function of time is recorded at the opposite end.